Bill Luecke: Calibrating my Powertap and SRM

Background

I pretend to be a metrologist at work, so when I bought my SRM from Will Wong, I knew I had a problem. I had two devices (a Powertap and an SRM) that measured the same (or nearly the same) value, and I could run them at the same time. It seemed unavoidable that I should compare them, and then ensure that they were as accurate as possible. I sheepishly admit that I ran the Powertap for an entire season without checking the calibration.

The internet has many good sources for how to do the calibration--see the list at the end.

Setup

I borrowed several calibrated masses from the lab, and a hanger I had lying around for calibrating load cells. Here's the bike in the workstand, with the rear brake locked with a jar of chamois cream.

Note--even though I work at the National Institute of Standards and Technology, the nation's metrology laboratory, that mass hanging off the pedal is W=20 lb. It's probably from the 1950s, though, when we didn't always follow the SI. ;-)

Devices

Powertap Pro 2012 hub, Garmin 500 reported calibration 11011
SRM wired, Dura Ace 7400(?) crank 53x39, L=172.5 mm, Powercontrol V unit S/N 16441 current calibration 34.3Nm/hz Age=?

Procedure: Powertap

Engage 39x25 to maximize torque sensitivity and level the crankarm by eye.
Wake up the powermeter.
Get to the calibration menu on the Garmin 500 (long enter press->Settings->Bike Settings->Tarmac->ANT+Power->Calibrate
Calibrate, wait for successful calibration,
Sequentially hang masses from hanger; record the torque values.

Procedure: SRM

Get to the auto-zero menu (Mode+Set press)
With no force applied, zero SRM by pressing "Set"
Sequentially hang masses from hanger, record frequency values

Results and Analysis

For the Powertap, the torque applied to the rear wheel, Ta, is

Ta = M g L /R

where M is the mass applied, g is the local acceleration of gravity, L is the crankarm length, and R is the gear ratio. For the SRM, the torque can be read directly without the gear ratio multiplier.

Not unsurprisingly, both devices are quite linear, so there's no point in showing plots of torque measured, Tm, vs torque applied, Ta. For the Powertap, I used R to compute a linear regression of the measured torque on the applied torque for the Ta>5 Nm. The regression was forced to include the origin:

lm(Tm~Ta+0,data=subset(cal,Type=="Powertap"&Tapplied>5),model=TRUE)

The results of that regression were interesting: the slope of the line, m is

m = (0.977+/-0.002) Nm

That is, the Powertap is reading about 2.2 % low. That's outside its stated limit of accuracy: +/-1.5 %.

For the SRM, the analysis is the same, except there is no gear multiplier and one plots the reported frequency, F, against the applied torque. A linear regression, not forced through zero, returned a slope, m,

m = (34.30 +/-0.06) Nm/hz

which is the current calibration value stored in the Powercontrol V head unit. Here's the residual plot:

Note that the residuals are on the order of 1 reading unit. The slight swaying of the masses as I added and removed them caused variations at least this large.

Conclusions and Limitations

The SRM calibration is dead on--fine German engineering.
The Powertap reads 2.2 % low, so the factory calibration should be adjusted.

I'm a bit concerned about the assertion about the Powertap calculation, since the residuals show some curvature, and the effective slope decreases at the largest torques. That could indicate more accurate readings at high torques. I have no idea what would produce curvature like that in what is essentially the output from a strain gage. The masses applied generate relatively small torques compared to those in use. Assume that you pedal at C=90 rpm, then the power, P, at the maximum calibration torque, T is

P = T w = 30 Nm * 2*pi radians/revolution * (1 minute/90 revolutions) * 60 s/min = 125 W

which is at the low end of the use range.

Next: getting the right calibration for the Powertap and fun things to do with with two powermeters.